Question

You can decrease the frequency of a standing wave on a string by __________.

Answer 1

making the string longer, using a thicker string, decreasing the tension

Answer 2

The n-th harmonic frequency of the standing wave is given by

$f_n=\frac{v}{\frac{2L}{n}} =\frac{nv}{2L}$.

Here $v=\sqrt{\frac{T}{m/L}}$, $T$ is tension in the string, $m$ is mass of the string and $L$ is the length of the string. Thus,

$f_n=\frac{v}{\frac{2L}{n}} =\frac{n\sqrt{\frac{T}{m/L}} }{2L}=\frac{n}{2} \sqrt{\frac{T}{mL}}$.

From the above equation, the frequency can be decreased by decreasing tension or increasing mass and length of the string.